A survey of several 10 to 11 year olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46 Construct the 98% confidence interval for the average amount spent by 10 to 11 year olds on a trip to the mall. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer 1

The 98% confidence interval for the average amount spent by 10 to 11-year-olds on a trip to the mall is 23.36 ± 2.933.

How to calculate the confidence interval and its critical value?

The confidence interval for a given level of percentage is given by

C. I = μ ± Z(σ/√n)

Where,

μ - mean, σ - standard deviation, n - sample size, and z - critical value.

The critical value is calculated by

step 1: 100% - (the confidence level)

step 2: Converting the step 1 result into decimal value

step 3: dividing the step 2 result by 2

This is indicated by α/2. So, from the normal distribution table, the z-value at α/2 is said to be the required critical value and denoted by Z_(α/2) or Z.

Calculation:

It is given that,

A survey of several 10 to 11-year-olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46

Sample size n = 6

Step 1: Finding the mean for the given amounts of the survey:

Mean μ = (18.31 + 25.09 + 26.96 + 26.54 + 21.84 + 21.46)/6

             = 23.36

Step 2: Finding the standard deviation:

Standard deviation σ = √summation(x - mean)²/n

On calculating, we get σ = 3.09

Step 3: Finding the critical value:

It is given that the confidence level is 98%

So, (100% - 98%) = 2%

Converting into decimal gives 0.02

So, α/2 = 0.02/2 = 0.01

Thus, at 0.01, the critical value Z = 2.326

Step 4: Constructing the confidence interval:

C.I = 23.36 ± (2.326) × (3.09/√6)

    = 23.36 ± (2.326 × 1.261)

    = 23.36 ± 2.933

So, the lower bound = 23.36 - 2.933 = 20.427

the upper bound = 23.36 + 2.933 =26.293

Therefore, the 98% confidence interval lies from 20.427 to 26.293.

Learn more about constructing the confidence interval here:

https://brainly.com/question/15714113

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Related Questions

Ming's school is selling tickets to a play. On the first day of ticket sales the school sold 8 adult tickets and 1 student ticket for a total of $95. The school took in $71 on the second day by selling 2 adult tickets and 7 student tickets. Define two variables for this situation. Write a system of equations to represent this situation. What is the price each of one adult ticket and one student ticket?

Answers

Answer:

Your answer.

8x + y = 95.........(1)

2x + 7y = 71........... (2)

Y = 95-8x........ (3)

Put this value in eq 2

Then x = 11

Put x value in eq 3

Y = 7

Thank you. And give my answer as Brainlist answer. Follow me for more

Step-by-step explanation:

-2x + 4 = -3x + 4
3
One Solution
No Solution
Infinite Solutions

Answers

Answer:

X=0 or no solution

Step-by-step explanation:

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move the variable to the left-hand side and change its sign

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Answers

Answer:

0

Step-by-step explanation:

Answer: -2.5

Step-by-step explanation:

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Answers

Answer:

10.5 hours!

Step-by-step explanation:

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There are 9 counters in a bag.

7 of the counters are green.
2 of the counters are blue.

Ria takes at random two counters from the bag.

Work out the probability that Ria takes one counter of each colour.

Answers

The Answer:
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Answers

The pair are parallel to eachother. The second equation in slope intercept form is y = 3x-3, since they have the same slope they’re parallel.
They are parallel!
When you put 2y=6x-6 into slope intercept form, you get y=3x-3.
They are parallel because they have the same slope.
Perpendicular lines have opposite reciprocal slope. For example, one equation would have a slope of 3 and the second one would have a slope of -1/3.
Hope that makes things more understandable!

What multiplication fact could help me find out 24 ÷ 8 ?

Answers

Answer:

Step-by-step explanation:

That would be 8 x 3. It would help because 24/8 = 3.

If we divide 24 by 8 it gives us the result of 3.

So a multiplication fact is 8x3 = 24.

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Answers

Answer:

x+3y=4x+y

Step-by-step explanation:

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Answers

Answer:

59.9%

Step-by-step explanation:

100/30 = 3.3

3.3*18 = 59.9%

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Answers

Answer:

The biggest one is 32 to 38

Step-by-step explanation:

hope it helps

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3 ft.
3 ft

Answers

Given:

The figure of a triangular prism.

To find:

The surface area of the triangular prism.

Solution:

We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.

Triangles have base 3 ft and height 2 ft.

Area of a triangle is

[tex]Area=\dfrac{1}{2}\times base\times height[/tex]

[tex]A_1=\dfrac{1}{2}\times (3)\times (2)[/tex]

[tex]A_1=3[/tex]

Area of congruent triangles are congruent. So,

[tex]A_1=A_2=3\text{ sq. units}[/tex]

Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.

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[tex]Area=Length\times width[/tex]

[tex]A_3=10\times 3[/tex]

[tex]A_3=30[/tex]

Dimensions of all three rectangles are same, therefore there areas are equal.

[tex]A_3=A_4=A_5=30[/tex]

Now, the total surface area of the prism is

[tex]A=A_1+A_2+A_3+A_4+A_5[/tex]

[tex]A=3+3+30+30+30[/tex]

[tex]A=96[/tex]

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Answers

Answer:

x=3.75

Step-by-step explanation:

-3/4x=-5

x-3    x-3

4x=15

/4   /4

x=3.75

Answer:

x = 3.75

Step-by-step explanation:

-3/4x = -5

(-3/4) -3/4x = -5(-3/4)

x = 3.75

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Answers

Answer:

a² - a² = 0

hope it helps

Answer:

a ² - a ²= 1 a ² - 1 a ² = 0

you understand ?

The candy store has a stock of candy. They have 15 bags of tootsie rolls, 10 boxes of nerds, 12 bags of gummy
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Answers

Answer:

15:49

Step-by-step explanation:

15 : 10+12+5+22

15 : 49

Can't be simplified further.

15:49 because it cannot be simplified

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Answers

Answer:

270 m³

Step-by-step explanation:

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Thank you whoever helps me!

Answers

Answer: To find the median, count the dots from left to right until you find the middle value.

Step-by-step explanation:

Ok so first it's not a dot line it's a dot plot. Second, let's define what a medium is. The medium is the "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. The middle number is 15, so the median is 15. Tip to find the median from a list of value ordered numbers every time cross a number from each side. For example, if you cross 13 from above also cross 26 and if you cross 23 then also cross 10.

Back to your original question of how to find the medium on a dot plot you need to take all the numbers from your dotted line put them in order even if they are repeated and then cross each one on each side from right to left. Also remember if you cross out all the numbers right and left and end up with two numbers left then take them and add them and then divide by 2 and that will be the median.

An example is attached on here in order to help you understand what I am saying. Hope this helps. Your welcome and I hope you make your mama proud.  

A medical provider is doing a study to determine the average time spent waiting before an appointment. The current average wait time is 34 minutes, which is 15% shorter than the average was when the study started. What was the average wait time then?

Answers

Answer:

39.1 minutes

Step-by-step explanation:

Given that:

Current wait time = 34 minutes

Current wait time is 15% shorter than average wait time when study started.

Average wait time when study started :

15% of current wait time :

0.15 * 34

= 5.1 minutes

Average wait time when study started :

34 minutes + 5.1 minutes

= 39.1 minutes

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Answers

8r^2 eight r squared hope this is right

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Answers

Answer:

$360.00

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Answers

Answer:

si porq si porq si si dices si es si

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Answers

Answer:

similar = only the angles are the same

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Answers

Answer:

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The ans is in the picture with the  steps how i got it

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Step-by-step explanation:

If you mean,

[tex] \frac{5}{2k} + 1 = - 9[/tex]

Then the answer would be,

[tex]k = - \frac{1}{4} [/tex]

But, if you mean

[tex] \frac{5}{2} k + 1 = - 9[/tex]

Then the answer would be,

[tex]k = - 4[/tex]

Was wondering if anyone knows the answer to part A and B for this question?

Answers

Answer:

no idea

Step-by-step explanation:

Answer:

k so from my opinion

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Answers

Answer:

25 cm

Step-by-step explanation:

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Answer:

i Don't understand what ur saying

Step-by-step explanation:

Answer:

Nagtatanong ka ba? kung ganun ano yun

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Answers

the answer is D

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Answers

Answer:

20 weeks

Step-by-step explanation:

1315$-415$=900$

900/45=20

Hence 20 weeks

Answer: 45b  

Step-by-step explanation: Divide 1315 with 45xb.

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Answers

Answer:

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Step-by-step explanation:

Look it up

X=40 will be the answer

In the figure shown the sum of the measures yxz and wxv is 75 degrees . what is the measure of zxw​

Answers

Answer: 105 = WXZ

Step-by-step explanation:

180 = WXZ + 75

subtract both sides by 75 and you get WXZ is equal to 105

I'm not 100% sure, lmk if I'm wrong

Factor the following expression completely.

2x^2y-18y

Answers

Answer:

Since both terms are perfect squares, factor using the difference of squares formula,

a2-b2=(a+b)(a−b) where a=x and b=3.2y(x+3)(x−3)

Step-by-step explanation:

hope this helps!!!

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